Numerical Methods for Time-dependent PDE's

Credits 8 credit points
Instructors Zegeling, P. (Universiteit Utrecht)
Prerequisites Basic knowledge of analysis, numerical analysis and some programming experience.
Aim To provide theoretical insight in, and to develop some practical skills for, numerical solution methods for evolutionary (time-dependent) partial differential equations (PDEs). Particular emphasis lies on finite difference and finite volume methods for parabolic and hyperbolic PDEs.
Description The following topics will be treated:
* Classification of PDEs, basic examples and applications
* Introduction to finite differences (FDs) & basic theory: convergence, consistency and stability
* The Lax theorem and Von Neumann stability analysis
* Dispersion, dissipation and modified PDEs
* FDs for parabolic equations in one and two space dimensions
* FDs and finite volume methods for hyperbolic equations (wave-type equations)
* The method-of-lines approach
* Non-uniform and adaptive moving grids
* Higher-order and spectral methods
* Nonstandard finite-differences
* Treatment of special PDE models, such as advection-diffusion-reaction equations, fractional-order, higher-order and Hamiltonian PDEs
Organization Lectures (2x 45 minutes) & excercise classes (1x 45 minutes).
Examination The final grade is based on homework assigments & programming assignments & a final test.
Literature Handouts & the books (both optional) W. Hundsdorfer & J.G. Verwer, Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations (Springer Series in Computational Mathematics, ISSN: 0179-3632) and Uri M. Ascher, Numerical Methods for Evolutionary Differential Equations (SIAM, 2008, Softcover, ISBN 978-0898716-52-8).
  Last changed: 02-02-2016 12:27